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Maximum tensile and compressive bending stresses in a beam

  • Thread starter dvep
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Homework Statement



Draw the shear force and bending moment diagrams for the beam shown in Fig. 1 below. Determine the maximum tensile and compressive bending stresses and the positions at which they occur. The beam’s cross-sectional area is shown in Fig. 2.

http://i1225.photobucket.com/albums/ee382/jon_jon_19/q2.jpg

Homework Equations



Bending Stress = Mc/I

Where I is inertia, c is distance from neutral axis, M is the bending moment

The Attempt at a Solution



I have drawn the shear and bending moment forces and worked out the moment of inertia in the T-section. But I am unsure how I work out the maximum tensile and compressive bending stresses.
How do I apply this.

Thanks.
 

Answers and Replies

  • #2
PhanthomJay
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I have drawn the shear and bending moment forces and worked out the moment of inertia in the T-section. But I am unsure how I work out the maximum tensile and compressive bending stresses.
How do I apply this.

Thanks.
On the assumption that you have correctly calculated the maximum moment and moment of inertia, max stress is My/I, where y is the distance from _____ to ______? The value of y will be differnt when calculating max tensile and max compressive stress.
 
  • #3
PhanthomJay
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I have attached a JPEG of the cross section where I have identified the composite parts.

I have worked the moment of inertias to be:

Ix^' = 440.333 x 10^3
Iy = 386.67 x 10^3

Itotal = Ix^' + Iy = 827.003 x 10^3
The bending stresses are about the axis that is horizontal to the cross section ( the x axis), thus you need to calculate and use Ix in your bending stress equations. You must not add up Ix and Iy. Also, your math is off, please recheck your numbers.
So for max tensile stress, would it be:

stress = (M x 42)/Itotal

For max compressive stress:

stress =(M x 18)/Itotal

Or is that completely wrong.

Would be grateful for your help, thanks.
You must of course also calculate M correctly...otherwise, you have the right approach for determining the max stresses.
 
  • #4
nvn
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dvep: You do not need to compute Iy, because there is no bending moment about the y axis. Your Ix value currently appears incorrect. Try again. Yes, M is the maximum moment in the bending moment diagram.
 
  • #5
nvn
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dvep: Your Ix value appears incorrect. Try again. Regarding the units of M, I recommend converting all units to N, mm, and MPa. Using N and mm, stresses will be N/mm^2, which is called and written MPa. Also, the bending stress formula is sigma = -M*y/Ix.
 
  • #6
nvn
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dvep: Nice work. You forgot to use y = 22 mm, and y = -38 mm. Try that again. Tensile stress is positive.

By the way, for long numbers having five or more digits, the international standard says you can write the digits in groups of three, separated by spaces. E.g., -15 000 000 N*mm, instead of -15000000 N*mm. See the international standard for writing units (ISO 31-0).
 
  • #7
nvn
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No, you forgot the negative sign in the bending stress formula, this time. Try again. Also, typically use asterisk for the multiplication symbol, instead of "x," because "x" can easily be confused with the variable x.
 
  • #8
nvn
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Last edited by a moderator:
  • #9
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dvep: Switch the words tensile and compressive, because tensile stress is positive. Also, in post 9, your units on M should be N*mm, not N*mm^2.

Thank you nvn, you were very helpful.
 
  • #10
nvn
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dvep: By the way, it is not allowed to delete your posts, the way you did, above. They call this abuse of the Edit feature. We will hopefully let it slide this time, since you are doing such excellent work. But I just wanted to warn you, so you can stay out of trouble, next time.

You did excellent work on your homework.
 
  • #11
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dvep: By the way, it is not allowed to delete your posts, the way you did, above. They call this abuse of the Edit feature. We will hopefully let it slide this time, since you are doing such excellent work. But I just wanted to warn you, so you can stay out of trouble, next time.

You did excellent work on your homework.
Oh, sorry I didn't know, I won't do it again.

Thank you again for you help.
 

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